Machine layout problem in flexible manufacturing systems
Operations Research
Methods for the one-dimensional space allocation problem
Computers and Operations Research
Generating lower bounds for the linear arrangement problem
Discrete Applied Mathematics
Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework
SIAM Journal on Optimization
Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization
SIAM Journal on Optimization
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
Semidefinite programming for discrete optimization and matrix completion problems
Discrete Applied Mathematics
Semidefinite Programming in the Space of Partial Positive Semidefinite Matrices
SIAM Journal on Optimization
A new lower bound for the single row facility layout problem
Discrete Applied Mathematics
Provably near-optimal solutions for very large single-row facility layout problems
Optimization Methods & Software - GLOBAL OPTIMIZATION
A particle swarm optimization for the single row facility layout problem
Computers and Industrial Engineering
Note: A polyhedral study of triplet formulation for single row facility layout problem
Discrete Applied Mathematics
Second-Order Cone Relaxations for Binary Quadratic Polynomial Programs
SIAM Journal on Optimization
Insertion based Lin-Kernighan heuristic for single row facility layout
Computers and Operations Research
A computational study and survey of methods for the single-row facility layout problem
Computational Optimization and Applications
A parallel ordering problem in facilities layout
Computers and Operations Research
A scatter search algorithm for the single row facility layout problem
Journal of Heuristics
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The facility layout problem is concerned with the arrangement of a given number of rectangular facilities so as to minimize the total cost associated with the (known or projected) interactions between them. We consider the one-dimensional space-allocation problem (ODSAP), also known as the single-row facility layout problem, which consists in finding an optimal linear placement of facilities with varying dimensions on a straight line. We construct a semidefinite programming (SDP) relaxation providing a lower bound on the optimal value of the ODSAP. To the best of our knowledge, this is the first non-trivial global lower bound for the ODSAP in the published literature. This SDP approach implicitly takes into account the natural symmetry of the problem and, unlike other algorithms in the literature, does not require the use of any explicit symmetry-breaking constraints. Furthermore, the structure of the SDP relaxation suggests a simple heuristic procedure which extracts a feasible solution to the ODSAP from the optimal matrix solution to the SDP relaxation. Computational results show that this heuristic yields a solution which is consistently within a few percentage points of the global optimal solution.